You mean like English as spoken in the American South, vs Australia, vs England? They are each very different from the English I speak, I can mostly understand each, but it takes effort and sometimes misunderstandings happen.
On the opposite side, consider the many "dialects" of Chinese: Mandarin, Cantonese, Shanghainese, Taiwanese, etc. Someone who only understands one of these will be pretty much entirely unable to understand the others. Yet we give the Chinese a nod and let them consider all these different languages to be just dialects.
But you wouldn't say Spanish and Portuguese are the same language.
I'd be more inclined to call Italian and Spanish the same language than Spanish and Portuguese from the little I know of them.
I know some BP and ES (though I'd never call myself remotely fluent in either), but I find EP quite difficult to follow, FWIW. I wouldn't be at all surprised if the mutual intelligibility of BP and Spanish is higher than EP and Spanish.
What defines a language? In the absence of context, I can't give you criteria for where the line is between a language or a dialect. But that doesn't matter, because the most important definition for "what's a language vs a dialect" is "how is it perceived by the world?". If the entire world thinks that Spanish and Portuguese are different languages, then they're different languages. It's that simple.
This isn't circular because I'm not saying "they're different languages because they're different languages". I'm saying "they're different languages because people say they're different languages".
But you can read it that way, if you want to.
A: A language has an army!
Examples: The Chinese government usually just talks about "Chinese". Mandarin is an English word to describe the Chinese language spoken in northern China--- but the Chinese government as political reasons to try to pretend that Cantonese is just a dialect.
Swedish, Danish and Norwegian are mutually intelligible, but each country has a government department dedicated to vetting books published in the language, and claim that what they speak are languages, not dialects.
I think the real answer is that taxonomy is difficult.
It is interesting to attend international events and watch the Scandinavians in their 60s or 70s speak among each other in their own languages with seemingly no problem, since their generation was pushed to overcome any hurdles to understanding the neighbours, while a group of younger Scandinavians that includes Danes is likely to switch to English because it just feels easier.